Nuprl Lemma : not-not-excluded-middle-quot-true
∀P:ℙ. (¬¬⇃(P ∨ (¬P)))
Proof
Definitions occuring in Statement :
quotient: x,y:A//B[x; y],
prop: ℙ,
all: ∀x:A. B[x],
not: ¬A,
or: P ∨ Q,
true: True
Definitions unfolded in proof :
false: False,
uimplies: b supposing a,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
or: P ∨ Q,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
implies: P ⇒ Q,
not: ¬A,
all: ∀x:A. B[x]
Lemmas referenced :
not-not-excluded-middle,
trivial-quotient-true,
equiv_rel_true,
true_wf,
or_wf,
quotient_wf,
not_wf
Rules used in proof :
dependent_functionElimination,
voidElimination,
independent_functionElimination,
universeEquality,
independent_isectElimination,
lambdaEquality,
sqequalRule,
hypothesis,
because_Cache,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}P:\mBbbP{}. (\mneg{}\mneg{}\00D9(P \mvee{} (\mneg{}P)))
Date html generated:
2017_04_14-AM-07_40_04
Last ObjectModification:
2017_04_11-AM-05_07_16
Theory : quot_1
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